In the majority of applications of conventional quantum theory
the information about dynamics (i.e.,
about the realistic self-adjoint
Hamiltonian \(\mathfrak {h}\) ) is
extracted, directly or indirectly, from the principle of
correspondence.
All interest in some unconventional,
crypto-Hermitian Hamiltonians emerges only
after one encounters some unsurmountable technical difficulties.
One then imagines that
the conventional formulations of quantum dynamics need not be optimal.
In such a situation, Dyson [1]}
found, purely empirically, that his calculations prove perceivably
simplified after a reformulation of the SP theory in which one would
work with two inner-product spaces (i.e., in our
present notation, with \({K}=2\) ).
